Stationary Rossby-wave ray envelope (source code)

= Stationary Rossby-wave ray envelope
{title2=$(x-Ut)^2+y^2\le(Ut)^2$}

For a uniform eastward current $U>0$ on a <beta plane> with $\beta>0$, stationary nondivergent <Rossby waves> have $k^2+l^2=\beta/U$. Their ground-frame <group velocity> is $2U(k^2,kl)/(k^2+l^2)$, tracing a circle centered at $(U,0)$ with radius $U$. Packets emitted by a localized source throughout $0<s<t$ occupy the disk shown in geometrical ray theory. This envelope is distinct from the full balanced near field. A westward current has no nontrivial stationary propagating branch in this model.